Chapter 3.6, Problem 51E

Solution

To find: what should be D’s monthly payment to achieve her goal.

$158.03

Given information:

D wants to accumulate $120,000 in 30 years by contributing to a money market account that earns 4.5% annual interest.

Formula Used:

Future Value of an Annuity

The future value FV of an annuity consisting of n equal periodic payments of R dollars at an interest rate i per compounding period (payment interval) is:

  $FV=R\frac{{\left(1+i\right)}^n-1}{i}$

Explanation:

The data given is:

  $FV=\$120,000,r=4.5\%,t=30,k=12$

Here, the interest is credited 12 times a year, so the interest rate is:

  $\begin{array}{c}i=\frac{r}{k}\\ =\frac{0.045}{12}\\ =0.00375\end{array}$

The number of payments is:

  $\begin{array}{c}n=k\cdot t\\ =12\cdot 30\\ =360\end{array}$

Let her monthly payment be $ R .

Substitute these values in the above formula,

  $\begin{array}{c}FV=R\frac{{\left(1+i\right)}^n-1}{i}\\ 120000=R\cdot \frac{{\left(1+0.00375\right)}^{360}-1}{0.00375}\\ 120000=R\left(759.39\right)\end{array}$

  $\begin{array}{c}R=\frac{120000}{759.39}\\ R\approx \$158.03\end{array}$

D’s monthly payment should be $158.03.